Warm-Up 11/19 Which equation is in Standard Form? (also called general form) Convert the equations to slope-intercept form (That means solve for y) x = 2y – 3 3x + 5y = 10

Opening 11/19 y = 2x+1 5x = 6+3y y/2 = 3 - x A linear equation is an equation for a straight line These are all linear equations: y = 2x+1 5x = 6+3y y/2 = 3 - x

Let’s look more closely at one example (written in slope-intercept form) The graph of y = 2x+1 is a straight line Description: When x increases, y increases  twice as fast, hence 2x slope is 2 When x is 0, y is already 1. Hence  +1 is also needed Y-intercept is 1 or (0,1) So: y = 2x + 1 (0,1)

Always Check for yourself that the line contains the points!! (0,1) Substitute in some x values to calculate (evaluate) the function, y x y = 2x + 1 -1 y = 2 (-1) + 1 = -1 y = 2 (0) + 1 = 1 1 y = 2 (1) + 1 = 3 2 3 (0,1) (0,1) (0,1) (0,1)

The variables (like "x" or "y") in Linear Equations do NOT have: Characteristics There are many ways of writing linear equations, but they usually have constants (like "2" or "c") and must have simple variables (like "x" or "y"). Examples: Non Examples:  The variables (like "x" or "y") in Linear Equations do NOT have: exponents  or roots y = 3x - 6 y - 2 = 3(x + 1) y + 2x - 2 = 0 5x = 6 y/2 = 3 y2 - 2 = 0 3√x - y = 6 x3/2 = 16

Other Common Forms The Identity Function This function is also called the “Linear Parent Function": y = x Point-Slope Form Used for a linear function when you know A point and the slope y - y1 = m(x - x1) Constant Functions It’s the graph of a horizontal line: y = #

Turn in your completion page to your teacher Work Time Your turn to practice Complete questions 1 – 10 Turn in your completion page to your teacher http://www.mathsisfun.com/equation_of_line.html

Journal Describe how to use the slope and y-intercept of a linear equation to graph the line. Also, explain the difference in the slopes and equations for horizontal and vertical lines